Rosette modes of oscillations of rotating stars caused by close degeneracies. III. JWKB analysis.

An asymptotic analysis is developed to describe rosette modes of oscillations in rotating stars, which have been recently discovered in numerical computations. The name of the modes comes from characteristic rosette patterns of the distributions of the kinetic-energy density on the meridional plane. As have been shown in the previous papers in this series, the physical reason for the formation of these modes is the rotation-induced interaction among several gravity modes with almost the same frequencies and successive spherical degrees of the same parity. This formation process is described in the framework of the quasi-degenerate perturbation theory. In this paper, the matrix eigenvalue problem, which appears in the perturbation analysis, is solved analytically, using asymptotic expressions of eigenfunctions, which are obtained by assuming that the wavelength of oscillations in the horizontal direction is sufficiently small. By further assuming that the number of interacting modes is large, simple expressions of the eigenfunctions and eigenfrequencies of rosette modes are obtained. Because these expressions can describe the essential part of characteristics of rosette modes, they are useful in understanding general properties of rosette modes that are common to any equilibrium structure. [ABSTRACT FROM PUBLISHER]